Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T18:16:38.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic results for a barrier potential model

Published online by Cambridge University Press:  15 May 2015

DAVID A. EDWARDS  and
CHRISTOPHER S. RAYMOND
DAVID A. EDWARDS
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA email: dedwards@udel.edu, craymond@udel.edu
CHRISTOPHER S. RAYMOND
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA email: dedwards@udel.edu, craymond@udel.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

An enhanced understanding of the microstructure of oxide ceramics will help scientists and engineers improve their efficiency and design. A phase-field model for the composition and phase distribution of the oxide ceramic components is studied. The model, which includes an obstacle in the phase portion of the energy potential, results in a minimisation problem that characterises the distribution of the bulk phases. The transition region between them is studied in several mathematically plausible asymptotic limits. The behaviour of the system in these limits provides insights into the applicability of the model and indicates appropriate parameter regimes.

Keywords

Phase-field modelAsymptoticsOxide ceramics
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 863 - 886
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Blowey, J. & Elliott, C. (1991) The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. Part I: Mathematical analysis. Eur. J. Appl. Math. 2, 233–280.CrossRefGoogle Scholar
[2]Brown, J. & Sobsey, M. D. (2009) Ceramic media amended with metal oxide for the capture of viruses in drinking water. Env. Tech. 30 (4), 379–391.CrossRefGoogle ScholarPubMed
[3]Cogswell, D. A. & Carter, W. C. (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: The possibility of metastable phases. Phys. Rev. E 83 (6, 1), 061602.CrossRefGoogle ScholarPubMed
[4]Grashchenkov, D. V., Balinova, Y. A. & Tinyakova, E. V. (2012) Aluminum oxide ceramic fibers and materials based on them. Glass Ceram. 69 (3–4), 130–133.CrossRefGoogle Scholar
[5]Heulens, J., Blanpain, B. & Moelans, N. (2011) A phase field model for isothermal crystallization of oxide melts. Acta Mater. 59, 2156–2165.CrossRefGoogle Scholar
[6]Keane, M. (2003) Ceramics for catalysis. J. Math. Sci. 38 (23), 4661–4675.CrossRefGoogle Scholar
[7]Kim, I. J. (2010) Thermal stability of Al2TiO5 ceramics for new diesel particulate filter applications-a literature review. J. Ceram. Proc. Res. 11 (4), 411–418.Google Scholar
[8]Nacken, M., Heidenreich, S., Hackel, M. & Schaub, G. (2007) Catalytic activation of ceramic filter elements for combined particle separation, NOx removal and VOC total oxidation. Appl. Catal. B 70 (1–4), 370–376.CrossRefGoogle Scholar
[9]Wei, G. C., Lapatovich, W. P., Browne, J. & Snellgrove, R. (2008) Dysprosium oxide ceramic arc tube for HID lamps. J. Phys. D 41 (4).CrossRefGoogle Scholar
[10]Wheeler, A. A., Boettinger, W. & McFadden, G. (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45, 7424–7439.CrossRefGoogle ScholarPubMed
[11]Wheeler, A. A., Boettinger, W. & McFadden, G. (1993) Phase-field model for solute trapping during solidification. Phys. Rev. E 47, 1893–1909.CrossRefGoogle ScholarPubMed